Related papers: On first-order model checking parameterized by the…
We prove that for every class $C$ of graphs with effectively bounded expansion, given a first-order sentence $\varphi$ and an $n$-element structure $\mathbb{A}$ whose Gaifman graph belongs to $C$, the question whether $\varphi$ holds in…
We study a natural variant of scheduling that we call \emph{partial scheduling}: In this variant an instance of a scheduling problem along with an integer $k$ is given and one seeks an optimal schedule where not all, but only $k$ jobs, have…
The cyclability of a graph is the maximum integer $k$ for which every $k$ vertices lie on a cycle. The algorithmic version of the problem, given a graph $G$ and a non-negative integer $k,$ decide whether the cyclability of $G$ is at least…
We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the…
This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and…
Most parameterized complexity classes are defined in terms of a parameterized version of the Boolean satisfiability problem (the so-called weighted satisfiability problem). For example, Downey and Fellow's W-hierarchy is of this form. But…
Given a class of graphs $\mathcal{H}$, the problem $\oplus\mathsf{Sub}(\mathcal{H})$ is defined as follows. The input is a graph $H\in \mathcal{H}$ together with an arbitrary graph $G$. The problem is to compute, modulo $2$, the number of…
We introduce tree-width for first order formulae \phi, fotw(\phi). We show that computing fotw is fixed-parameter tractable with parameter fotw. Moreover, we show that on classes of formulae of bounded fotw, model checking is fixed…
It is not hard to write a first order formula which is true for a given graph G but is false for any graph not isomorphic to G. The smallest number $(G) of nested quantifiers in a such formula can serve as a measure for the ``first order…
A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered parameter is informed by the theoretical relations between…
We construct a fixed parameter algorithm parameterized by d and k that takes as an input a graph G' obtained from a d-degenerate graph G by complementing on at most k arbitrary subsets of the vertex set of G and outputs a graph H such that…
A decision problem is called parameterized if its input is a pair of strings. One of these strings is referred to as a parameter. The problem: given a propositional logic program P and a non-negative integer k, decide whether P has a stable…
It is known that for subgraph-closed graph classes the first-order model checking problem is fixed-parameter tractable if and only if the class is nowhere dense [Grohe, Kreutzer, Siebertz, STOC 2014]. However, the dependency on the formula…
Given two graphs $H$ and $G$, the Subgraph Isomorphism problem asks if $H$ is isomorphic to a subgraph of $G$. While NP-hard in general, algorithms exist for various parameterized versions of the problem: for example, the problem can be…
The classical zero-one law for first-order logic on random graphs says that for any first-order sentence $\phi$ in the theory of graphs, as n approaches infinity, the probability that the random graph G(n, p) satisfies $\phi$ approaches…
Kuske and Schweikardt introduced the very expressive first-order counting logic FOC(P) to model database queries with counting operations. They showed that there is an efficient model-checking algorithm on graphs with bounded degree, while…
Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA '14], we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, $K_t$-free unit…
We say that a first order formula A distinguishes a graph G from another graph G' if A is true on G and false on G'. Provided G and G' are non-isomorphic, let D(G,G') denote the minimal quantifier rank of a such formula. We prove that, if G…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
It is well known [Lov\'asz, 67] that up to isomorphism a graph~$G$ is determined by the homomorphism counts $\hom(F, G)$, i.e., the number of homomorphisms from $F$ to $G$, where $F$ ranges over all graphs. Thus, in principle, we can answer…